Implement Polyhedron::Contains Intersects ContainsConvex ClosestPoint IsNull
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@@ -11,7 +11,7 @@ namespace J3ML::Geometry
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using namespace J3ML::LinearAlgebra;
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// Represents a three-dimensional closed geometric solid defined by flat polygonal faces.
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class Polyhedron : public Shape
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class Polyhedron
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{
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public:
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// Stores a list of indices of a single face of a Polygon
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@@ -33,78 +33,101 @@ namespace J3ML::Geometry
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// Specifies the vertices of this polyhedron.
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std::vector<Vector3> v;
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std::vector<Face> f;
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public:
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/// The default constructor creates a null polyhedron.
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/** The null polyhedron has 0 vertices and 0 faces.
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@see IsNull(). */
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Polyhedron() = default;
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int NumVertices() const {return (int)v.size();}
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int NumFaces() const { return (int)f.size();}
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AABB MinimalEnclosingAABB() const;
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[[nodiscard]] int NumVertices() const {return (int)v.size();}
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[[nodiscard]] int NumFaces() const { return (int)f.size();}
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[[nodiscard]] AABB MinimalEnclosingAABB() const;
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Vector3 Vertex(int vertexIndex) const;
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[[nodiscard]] Vector3 Vertex(int vertexIndex) const;
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[[nodiscard]] bool Contains(const Vector3&) const;
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[[nodiscard]] bool Contains(const LineSegment&) const;
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[[nodiscard]] bool Contains(const Triangle&) const;
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[[nodiscard]] bool Contains(const Polygon&) const;
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[[nodiscard]] bool Contains(const AABB&) const;
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[[nodiscard]] bool Contains(const OBB&) const;
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[[nodiscard]] bool Contains(const Frustum&) const;
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[[nodiscard]] bool Contains(const Polyhedron&) const;
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[[nodiscard]] bool ContainsConvex(const Vector3&, float epsilon = 1e-4f) const;
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[[nodiscard]] bool ContainsConvex(const LineSegment&) const;
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[[nodiscard]] bool ContainsConvex(const Triangle&) const;
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/// Tests whether this polyhedron and the given object intersect.
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/** Both objects are treated as "solid", meaning that if one of the objects is fully contained inside
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another, this function still returns true. (e.g. in case a line segment is contained inside this polyhedron,
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or this polyhedron is contained inside a sphere, etc.)
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@return True if an intersection occurs or one of the objects is contained inside the other, false otherwise.
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@note This function assumes that this polyhedron is closed and the edges are not self-intersecting.
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@see Contains(), ContainsConvex(), ClosestPoint(), ClosestPointConvex(), Distance(), IntersectsConvex().
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@todo Add Intersects(Circle/Disc). */
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[[nodiscard]] bool Intersects(const Line&) const;
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[[nodiscard]] bool Intersects(const LineSegment&) const;
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[[nodiscard]] bool Intersects(const Ray&) const;
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[[nodiscard]] bool Intersects(const Plane&) const;
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[[nodiscard]] bool Intersects(const Polyhedron&) const;
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[[nodiscard]] bool Intersects(const AABB& aabb) const;
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[[nodiscard]] bool Intersects(const OBB&) const;
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[[nodiscard]] bool Intersects(const Triangle&) const;
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[[nodiscard]] bool Intersects(const Polygon&) const;
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[[nodiscard]] bool Intersects(const Frustum&) const;
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[[nodiscard]] bool Intersects(const Sphere&) const;
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[[nodiscard]] bool Intersects(const Capsule& capsule) const;
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[[nodiscard]] bool IsClosed() const;
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[[nodiscard]] Plane FacePlane(int faceIndex) const;
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[[nodiscard]] std::vector<Polygon> Faces() const;
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[[nodiscard]] int NumEdges() const;
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[[nodiscard]] LineSegment Edge(int edgeIndex) const;
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[[nodiscard]] std::vector<std::pair<int, int>> EdgeIndices() const;
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[[nodiscard]] std::vector<LineSegment> Edges() const;
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[[nodiscard]] Polygon FacePolygon(int faceIndex) const;
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[[nodiscard]] Vector3 FaceNormal(int faceIndex) const;
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[[nodiscard]] bool IsConvex() const;
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/// Returns true if the Euler formula (V + F - E == 2) holds for this Polyhedron.
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/** The running time is O(E) ~ O(V).
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@see NumVertices(), NumEdges(), NumFaces(). */
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[[nodiscard]] bool EulerFormulaHolds() const;
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bool Contains(const Vector3&) const;
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bool Contains(const LineSegment&) const;
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bool Contains(const Triangle&) const;
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bool Contains(const Polygon&) const;
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bool Contains(const AABB&) const;
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bool Contains(const OBB&) const;
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bool Contains(const Frustum&) const;
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bool Contains(const Polyhedron&) const;
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[[nodiscard]] Vector3 ApproximateConvexCentroid() const;
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bool ContainsConvex(const Vector3&, float epsilon = 1e-4f) const;
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bool ContainsConvex(const LineSegment&) const;
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bool ContainsConvex(const Triangle&) const;
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[[nodiscard]] int ExtremeVertex(const Vector3 &direction) const;
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bool Intersects(const Line&) const;
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bool Intersects(const LineSegment&) const;
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bool Intersects(const Ray&) const;
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bool Intersects(const Plane&) const;
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bool Intersects(const Polyhedron&) const;
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bool Intersects(const AABB&) const;
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bool Intersects(const OBB&) const;
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bool Intersects(const Triangle&) const;
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bool Intersects(const Polygon&) const;
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bool Intersects(const Frustum&) const;
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bool Intersects(const Sphere&) const;
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bool Intersects(const Capsule& capsule) const;
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bool IsClosed() const;
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Plane FacePlane(int faceIndex) const;
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std::vector<Polygon> Faces() const;
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int NumEdges() const;
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LineSegment Edge(int edgeIndex) const;
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std::vector<std::pair<int, int>> EdgeIndices() const;
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std::vector<LineSegment> Edges() const;
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Polygon FacePolygon(int faceIndex) const;
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Vector3 FaceNormal(int faceIndex) const;
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bool IsConvex() const;
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Vector3 ApproximateConvexCentroid() const;
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int ExtremeVertex(const Vector3 &direction) const;
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Vector3 ExtremePoint(const Vector3 &direction) const;
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[[nodiscard]] Vector3 ExtremePoint(const Vector3 &direction) const;
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/// Tests if the given face of this Polyhedron contains the given point.
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bool FaceContains(int faceIndex, const Vector3 &worldSpacePoint, float polygonThickness = 1e-3f) const;
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[[nodiscard]] bool FaceContains(int faceIndex, const Vector3 &worldSpacePoint, float polygonThickness = 1e-3f) const;
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/// A helper for Contains() and FaceContains() tests: Returns a positive value if the given point is contained in the given face,
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/// and a negative value if the given point is outside the face. The magnitude of the return value reports a pseudo-distance
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/// from the point to the nearest edge of the face polygon. This is used as a robustness/stability criterion to estimate how
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/// numerically believable the result is.
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float FaceContainmentDistance2D(int faceIndex, const Vector3 &worldSpacePoint, float polygonThickness = 1e-5f) const;
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[[nodiscard]] float FaceContainmentDistance2D(int faceIndex, const Vector3 &worldSpacePoint, float polygonThickness = 1e-5f) const;
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void ProjectToAxis(const Vector3 &direction, float &outMin, float &outMax) const;
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Vector3 ClosestPoint(const LineSegment& lineSegment, Vector3 *lineSegmentPt) const;
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[[nodiscard]] Vector3 ClosestPoint(const Vector3& point) const;
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/// Returns true if this polyhedron has 0 vertices and 0 faces.
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bool IsNull() const { return v.empty() && f.empty(); }
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protected:
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private:
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};
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@@ -1,5 +1,5 @@
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#include <J3ML/Geometry/Polyhedron.h>
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#include <J3ML/Geometry/AABB.h>
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#include <J3ML/Geometry/AABB.hpp>
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#include <J3ML/Geometry/Triangle.h>
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#include <J3ML/Geometry/LineSegment.h>
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#include "J3ML/Geometry/Ray.h"
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@@ -508,6 +508,8 @@ namespace J3ML::Geometry
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return true;
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}
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bool Polyhedron::EulerFormulaHolds() const { return NumVertices() + NumFaces() - NumEdges() == 2;}
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bool Polyhedron::ContainsConvex(const Vector3 &point, float epsilon) const
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{
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assert(IsConvex());
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@@ -638,6 +640,64 @@ namespace J3ML::Geometry
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return false;
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}
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template <typename T>
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bool PolyhedronIntersectsAABB_OBB(const Polyhedron& p, const T& obj) {
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if (p.Contains(obj.CenterPoint()))
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return true;
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if (obj.Contains(p.ApproximateConvexCentroid())) // @bug: This is not correct for concave polyhedrons!
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return true;
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// Test for each edge of the AABB / OBB whether this polyhedron intersects it.
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for(int i = 0; i < obj.NumEdges(); ++i)
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if (p.Intersects(obj.Edge(i)))
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return true;
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// Test for each edge of this polyhedron whether the AABB / OBB intersects it.
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for(size_t i = 0; i < p.f.size(); ++i)
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{
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assert(!p.f[i].v.empty()); // Cannot have degenerate faces here, and for performance reasons, don't start checking for this condition in release mode!
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int v0 = p.f[i].v.back();
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Vector3 l0 = p.v[v0];
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for(size_t j = 0; j < p.f[i].v.size(); ++j)
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{
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int v1 = p.f[i].v[j];
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Vector3 l1 = p.v[v1];
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if (v0 < v1 && obj.Intersects(LineSegment(l0, l1))) // If v0 < v1, then this line segment is the canonical one.
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return true;
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l0 = l1;
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v0 = v1;
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}
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}
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return false;
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}
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bool Polyhedron::Intersects(const AABB &aabb) const {
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return PolyhedronIntersectsAABB_OBB(*this, aabb);
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}
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bool Polyhedron::Intersects(const OBB& obb) const {
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return PolyhedronIntersectsAABB_OBB(*this, obb);
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}
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bool Polyhedron::Intersects(const Frustum& obb) const {
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return PolyhedronIntersectsAABB_OBB(*this, obb);
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}
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bool Polyhedron::Intersects(const Triangle& obb) const {
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return PolyhedronIntersectsAABB_OBB(*this, obb);
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}
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bool Polyhedron::Intersects(const Sphere& sphere) const {
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Vector3 closestPt = ClosestPoint(sphere.Position);
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return closestPt.DistanceSq(sphere.Position) <= sphere.Radius * sphere.Radius;
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}
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bool Polyhedron::Intersects(const Polygon& polygon) const {
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return Intersects(polygon.ToPolyhedron());
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}
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bool Polyhedron::Intersects(const Capsule &capsule) const {
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Vector3 pt, ptOnLineSegment;
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pt = ClosestPoint(capsule.l, &ptOnLineSegment);
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@@ -677,6 +737,22 @@ namespace J3ML::Geometry
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return closestPt;
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}
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Vector3 Polyhedron::ClosestPoint(const Vector3 &point) const {
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if (Contains(point))
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return point;
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Vector3 closestPoint = Vector3::NaN;
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float closestDistance = Math::Infinity;
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for (int i = 0; i < NumFaces(); ++i) {
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Vector3 closestOnPoly = FacePolygon(i).ClosestPoint(point);
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float d = closestOnPoly.DistanceSq(point);
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if (d < closestDistance) {
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closestPoint = closestOnPoly;
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closestDistance = d;
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}
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}
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return closestPoint;
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}
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}
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